(x-1)(x+(1+i))(x+(1-i))=0

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Solution for (x-1)(x+(1+i))(x+(1-i))=0 equation: 


Simplifying
(x + -1)(x + (1 + i))(x + (1 + -1i)) = 0

Reorder the terms:
(-1 + x)(x + (1 + i))(x + (1 + -1i)) = 0

Remove parenthesis around (1 + i)
(-1 + x)(x + 1 + i)(x + (1 + -1i)) = 0

Reorder the terms:
(-1 + x)(1 + i + x)(x + (1 + -1i)) = 0

Remove parenthesis around (1 + -1i)
(-1 + x)(1 + i + x)(x + 1 + -1i) = 0

Reorder the terms:
(-1 + x)(1 + i + x)(1 + -1i + x) = 0

Multiply (-1 + x) * (1 + i + x)
(-1(1 + i + x) + x(1 + i + x))(1 + -1i + x) = 0
((1 * -1 + i * -1 + x * -1) + x(1 + i + x))(1 + -1i + x) = 0
((-1 + -1i + -1x) + x(1 + i + x))(1 + -1i + x) = 0
(-1 + -1i + -1x + (1 * x + i * x + x * x))(1 + -1i + x) = 0

Reorder the terms:
(-1 + -1i + -1x + (ix + 1x + x2))(1 + -1i + x) = 0
(-1 + -1i + -1x + (ix + 1x + x2))(1 + -1i + x) = 0

Reorder the terms:
(-1 + -1i + ix + -1x + 1x + x2)(1 + -1i + x) = 0

Combine like terms: -1x + 1x = 0
(-1 + -1i + ix + 0 + x2)(1 + -1i + x) = 0
(-1 + -1i + ix + x2)(1 + -1i + x) = 0

Multiply (-1 + -1i + ix + x2) * (1 + -1i + x)
(-1(1 + -1i + x) + -1i * (1 + -1i + x) + ix(1 + -1i + x) + x2(1 + -1i + x)) = 0
((1 * -1 + -1i * -1 + x * -1) + -1i * (1 + -1i + x) + ix(1 + -1i + x) + x2(1 + -1i + x)) = 0
((-1 + 1i + -1x) + -1i * (1 + -1i + x) + ix(1 + -1i + x) + x2(1 + -1i + x)) = 0
(-1 + 1i + -1x + (1 * -1i + -1i * -1i + x * -1i) + ix(1 + -1i + x) + x2(1 + -1i + x)) = 0

Reorder the terms:
(-1 + 1i + -1x + (-1i + -1ix + 1i2) + ix(1 + -1i + x) + x2(1 + -1i + x)) = 0
(-1 + 1i + -1x + (-1i + -1ix + 1i2) + ix(1 + -1i + x) + x2(1 + -1i + x)) = 0
(-1 + 1i + -1x + -1i + -1ix + 1i2 + (1 * ix + -1i * ix + x * ix) + x2(1 + -1i + x)) = 0

Reorder the terms:
(-1 + 1i + -1x + -1i + -1ix + 1i2 + (1ix + ix2 + -1i2x) + x2(1 + -1i + x)) = 0
(-1 + 1i + -1x + -1i + -1ix + 1i2 + (1ix + ix2 + -1i2x) + x2(1 + -1i + x)) = 0
(-1 + 1i + -1x + -1i + -1ix + 1i2 + 1ix + ix2 + -1i2x + (1 * x2 + -1i * x2 + x * x2)) = 0

Reorder the terms:
(-1 + 1i + -1x + -1i + -1ix + 1i2 + 1ix + ix2 + -1i2x + (-1ix2 + 1x2 + x3)) = 0
(-1 + 1i + -1x + -1i + -1ix + 1i2 + 1ix + ix2 + -1i2x + (-1ix2 + 1x2 + x3)) = 0

Reorder the terms:
(-1 + 1i + -1i + -1ix + 1ix + ix2 + -1ix2 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0

Combine like terms: 1i + -1i = 0
(-1 + 0 + -1ix + 1ix + ix2 + -1ix2 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0
(-1 + -1ix + 1ix + ix2 + -1ix2 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0

Combine like terms: -1ix + 1ix = 0
(-1 + 0 + ix2 + -1ix2 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0
(-1 + ix2 + -1ix2 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0

Combine like terms: ix2 + -1ix2 = 0
(-1 + 0 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0
(-1 + 1i2 + -1i2x + -1x + 1x2 + x3) = 0

Solving
-1 + 1i2 + -1i2x + -1x + 1x2 + x3 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1i2 + -1i2x + -1x + 1x2 + 1 + x3 = 0 + 1

Reorder the terms:
-1 + 1 + 1i2 + -1i2x + -1x + 1x2 + x3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1i2 + -1i2x + -1x + 1x2 + x3 = 0 + 1
1i2 + -1i2x + -1x + 1x2 + x3 = 0 + 1

Combine like terms: 0 + 1 = 1
1i2 + -1i2x + -1x + 1x2 + x3 = 1

Add 'x' to each side of the equation.
1i2 + -1i2x + -1x + 1x2 + x + x3 = 1 + x

Reorder the terms:
1i2 + -1i2x + -1x + x + 1x2 + x3 = 1 + x

Combine like terms: -1x + x = 0
1i2 + -1i2x + 0 + 1x2 + x3 = 1 + x
1i2 + -1i2x + 1x2 + x3 = 1 + x

Add '-1x2' to each side of the equation.
1i2 + -1i2x + 1x2 + -1x2 + x3 = 1 + x + -1x2

Combine like terms: 1x2 + -1x2 = 0
1i2 + -1i2x + 0 + x3 = 1 + x + -1x2
1i2 + -1i2x + x3 = 1 + x + -1x2

Add '-1x3' to each side of the equation.
1i2 + -1i2x + x3 + -1x3 = 1 + x + -1x2 + -1x3

Combine like terms: x3 + -1x3 = 0
1i2 + -1i2x + 0 = 1 + x + -1x2 + -1x3
1i2 + -1i2x = 1 + x + -1x2 + -1x3

Reorder the terms:
-1 + 1i2 + -1i2x + -1x + x2 + x3 = 1 + x + -1x2 + -1x3 + -1 + -1x + x2 + x3

Reorder the terms:
-1 + 1i2 + -1i2x + -1x + x2 + x3 = 1 + -1 + x + -1x + -1x2 + x2 + -1x3 + x3

Combine like terms: 1 + -1 = 0
-1 + 1i2 + -1i2x + -1x + x2 + x3 = 0 + x + -1x + -1x2 + x2 + -1x3 + x3
-1 + 1i2 + -1i2x + -1x + x2 + x3 = x + -1x + -1x2 + x2 + -1x3 + x3

Combine like terms: x + -1x = 0
-1 + 1i2 + -1i2x + -1x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3
-1 + 1i2 + -1i2x + -1x + x2 + x3 = -1x2 + x2 + -1x3 + x3

Combine like terms: -1x2 + x2 = 0
-1 + 1i2 + -1i2x + -1x + x2 + x3 = 0 + -1x3 + x3
-1 + 1i2 + -1i2x + -1x + x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-1 + 1i2 + -1i2x + -1x + x2 + x3 = 0

The solution to this equation could not be determined.

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